Lifting group actions and nonnegative curvature

DOI10.1090/S0002-9947-2011-05272-4zbMath1219.53051arXiv0801.0767MaRDI QIDQ3004355

Wolfgang Ziller, Karsten Grove

Publication date: 1 June 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.0767

zbMATH Keywords

principal bundlenonnegative sectional curvaturecohomogeneity one manifold

Mathematics Subject Classification ID

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Issues of holonomy in differential geometry (53C29)

Related Items

Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension ⋮ Vector bundles of non-negative curvature over cohomogeneity one manifolds ⋮ Strongly nonnegative curvature ⋮ Some new examples with almost positive curvature ⋮ Polar manifolds and actions ⋮ A panoramic glimpse of manifolds with sectional curvature bounded from below ⋮ Differentiable classification of 4-manifolds with singular Riemannian foliations ⋮ Nonnegative curvature on stable bundles over compact rank one symmetric spaces ⋮ Topology of non-negatively curved manifolds ⋮ Flats and submersions in non-negative curvature ⋮ Higgs bundles and exceptional isogenies ⋮ Open manifolds with non-homeomorphic positively curved souls ⋮ Curvature homogeneous manifolds in dimension 4 ⋮ On the moduli spaces of metrics with nonnegative sectional curvature ⋮ The stable converse soul question for positively curved homogeneous spaces ⋮ Index theory and deformations of open nonnegatively curved manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a compact Lie group acting on a manifold
• Classification of cohomogeneity one manifolds in low dimensions
• 4-dimensional G-manifolds with 3-dimensional orbits
• Four-manifolds with positive curvature operator
• Vector bundles on complex projective spaces
• Geodesic spheres as generators of the homotopy groups of O,BO
• Equivariant bundles
• On the fundamental groups of positively curved manifolds
• Curvature and symmetry of Milnor spheres
• Cheeger manifolds and the classification of biquotients.
• On complete metrics of nonnegative curvature on 2-plane bundles
• Topology of non-negatively curved manifolds
• Classification of oriented sphere bundles over a 4-complex
• Positively curved cohomogeneity one manifolds and 3-Sasakian geometry
• On compact subgroups of the diffeomorphism groups of Kervaire spheres
• Faserbündel mit Gruppenoperation
• On the structure of complete manifolds of nonnegative curvature
• Lifting group actions in fibre bundles
• The Cohomology of Differentiable Transformation Groups
• Equivariant Geometry and Kervaire Spheres
• Unflat Connections in 3-Sphere Bundles Over S 4
• Characteristic Classes. (AM-76)
• Vector Bundles with No Soul
• EQUIVARIANT PRINCIPAL BUNDLES OVER SPHERES AND COHOMOGENEITY ONE MANIFOLDS
• Obstructions to nonnegative curvature and rational homotopy theory
• Topological obstructions to nonnegative curvature